Question

Conservationists will take snow geese off the endangered species list when the population hits 10,000. If populations are sustaining growth at r = 0.088 and the population in 2001 is 3000 individuals, in what year will snow geese be taken off the endangered species list?

A) between 2106 and 2109

B) between 2009 and 2012

C) between 2012 and 2015

D) between 2015 and 2018

The answer is C, but can someone please show which formula to use and how you got to final answer?

Answer 1

Answer:

C) between 2012 and 2015

Explanation:

The population of snow geese as a function of the time 't' in years is given by the following equation:

$P(t) = 3000*e^{0.088t}$

With t=0 happening in 2001

For the snow geese to be taken off the endangered species list, P(t) = 10,000:

$10,000= 3000*e^{0.088t}\\ln(10,000) = ln(3000) + ln(e^{0.088t})\\ln(10,000) = ln(3000) + 0.088t*ln(e)\\\\t=\frac{ln(10,000) - ln(3000)}{0.088}\\t=13.68 \ years$

The population will reach 10,000 animals 13.68 years after 2001, that is "2014.68". This means that the population will reach 10,000 between 2014 and 2015.

Therefore, the answer is C) between 2012 and 2015